Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type
are presented as a useful approach for the description of transport dynamics in complex …

The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

A transport equation that uses fractional‐order dispersion derivatives has fundamental
solutions that are Lévy's α‐stable densities. These densities represent plumes that spread …

Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a
reformulation of continuum mechanics based on integration of interactions rather than …

This monograph is an invitation both to the interested scientists and the engineers. It
presents a thorough introduction to the recent results of local fractional calculus. It is also …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

A recently developed nonlocal vector calculus is exploited to provide a variational analysis
for a general class of nonlocal diffusion problems described by a linear integral equation on …

A governing equation of stable random walks is developed in one dimension. This Fokker‐
Planck equation is similar to, and contains as a subset, the second‐order advection …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …